Question

$f$ is holomorphic in Ω such that $|f|^2$ is harmonic; we need to show that $f$ is constant.

score 1.1k · Answer 1 · 2016-05-07 17:59:35

1.1k

Views

$f$ is holomorphic in Ω such that $|f|^2$ is harmonic; we need to show that $f$ is constant.

Published on 07 May 2016 - 17:59

score 31 · Answer 2 · 2016-05-07 20:36:45

31

Views

need an example of an open set $V$ and a holomorphic function $f$ on $V$

Published on 07 May 2016 - 20:36

score 191 · Answer 3 · 2016-05-09 19:58:37

191

Views

If $f^3,~\bar{f}^2$ are holomorphic on a domain $D$, then $f$ is constant on $D$.

Published on 09 May 2016 - 19:58

score 136 · Answer 4 · 2016-05-10 20:18:15

136

Views

$ f(z) = \int _{0} ^\infty e^{-z t^2} dt $ is holomorphic in $Re(z) > 0$

Published on 10 May 2016 - 20:18

score 618 · Answer 5 · 2026-02-27 04:24:52

618

Views

f holomorphic in an annulus can be written as $f(z)=z^{n}\,e^{g(z)}$

Published on 27 Feb 2026 - 4:24

score 341 · Answer 6 · 2016-05-13 18:30:34

341

Views

Meaning of $f$ being holomorphic on the neighborhood of the unit disc, and Cauchy Theorem

Published on 13 May 2016 - 18:30

score 478 · Answer 7 · 2016-05-15 00:28:47

478

Views

Is a modular form on $\text{SL}_2(\mathbb{Z})$ also a modular form on congruence subgroups?

Published on 15 May 2016 - 0:28

score 84 · Answer 8 · 2016-05-16 01:47:13

84

Views

Give a conformal map, with certain initial conditions, from the open unit disc to another open set ...

Published on 16 May 2016 - 1:47

score 538 · Answer 9 · 2016-05-17 00:39:57

538

Views

Principle of the Argument: How do I get the $\Delta{\arg f(z)}$?

Published on 17 May 2016 - 0:39

score 224 · Answer 10 · 2016-05-17 17:37:01

224

Views

Construction of function holomorphic in $\mathbb{C}\setminus\{0, 1\}$ satisfying specific conditions

Published on 17 May 2016 - 17:37

score 405 · Answer 11 · 2016-05-17 20:55:32

405

Views

Injectivity of the evaluation map from holomorphic functions to a Banach algebra

Published on 17 May 2016 - 20:55

score 87 · Answer 12 · 2016-05-19 12:34:08

87

Views

Claim about holomorphic extension

Published on 19 May 2016 - 12:34

score 305 · Answer 13 · 2026-03-27 02:08:28

305

Views

Can a holomorphic function vanish on an infinite 2D rectangular grid?

Published on 27 Mar 2026 - 2:08

score 323 · Answer 14 · 2026-03-27 02:07:39

323

Views

entire function with $f(n)=n^2$ for integers $n$

Published on 27 Mar 2026 - 2:07

score 181 · Answer 15 · 2016-05-24 20:58:17

181

Views

A holomorphic function $f:D\rightarrow D$ such that $\mid f(z^2)\mid\geq \mid f(z)\mid$ for all $z$ must be constant.

Published on 24 May 2016 - 20:58

List Question

$f$ is holomorphic in Ω such that $|f|^2$ is harmonic; we need to show that $f$ is constant.

need an example of an open set $V$ and a holomorphic function $f$ on $V$

If $f^3,~\bar{f}^2$ are holomorphic on a domain $D$, then $f$ is constant on $D$.

$ f(z) = \int _{0} ^\infty e^{-z t^2} dt $ is holomorphic in $Re(z) > 0$

f holomorphic in an annulus can be written as $f(z)=z^{n}\,e^{g(z)}$

Meaning of $f$ being holomorphic on the neighborhood of the unit disc, and Cauchy Theorem

Is a modular form on $\text{SL}_2(\mathbb{Z})$ also a modular form on congruence subgroups?

Give a conformal map, with certain initial conditions, from the open unit disc to another open set ...

Principle of the Argument: How do I get the $\Delta{\arg f(z)}$?

Construction of function holomorphic in $\mathbb{C}\setminus\{0, 1\}$ satisfying specific conditions

Injectivity of the evaluation map from holomorphic functions to a Banach algebra

Claim about holomorphic extension

Can a holomorphic function vanish on an infinite 2D rectangular grid?

entire function with $f(n)=n^2$ for integers $n$

A holomorphic function $f:D\rightarrow D$ such that $\mid f(z^2)\mid\geq \mid f(z)\mid$ for all $z$ must be constant.

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